A wholesaler had 200 dozens of mangoes. He sold some of these mangoes at 20% profit and the rest at 10% profit, so that he made 13% profit on selling all the mangoes. How many mangoes (in dozens) did he sell at 20% profit?

Options

A. 140
B. 60
C. 80
D. 120

Answer

To solve the problem step by step, we can use the concept of allegations to find out how many dozens of mangoes were sold at a 20% profit.

### Step 1: Understand the given information
- The wholesaler has 200 dozens of mangoes.
- Some mangoes are sold at a 20% profit, and the rest at a 10% profit.
- The overall profit from selling all the mangoes is 13%.

### Step 2: Set up the profit percentages
- Profit at first selling price = 20%
- Profit at second selling price = 10%
- Overall profit = 13%

### Step 3: Calculate the differences in profits
- Difference between 20% and 13% = 20% - 13% = 7%
- Difference between 10% and 13% = 13% - 10% = 3%

### Step 4: Set up the ratio using allegations
Using the method of allegations, we can find the ratio of the quantities sold at different profit percentages:
- The ratio of the quantities sold at 20% profit to those sold at 10% profit is given by the differences calculated:
- Ratio = Difference at 10% : Difference at 20% = 3 : 7

### Step 5: Calculate the total parts in the ratio
- Total parts = 3 + 7 = 10

### Step 6: Find the value of each part
- Total dozens of mangoes = 200
- Value of one part = Total dozens / Total parts = 200 / 10 = 20 dozens

### Step 7: Calculate the number of dozens sold at 20% profit
- Since the ratio for 20% profit is 3 parts:
- Number of dozens sold at 20% profit = 3 parts × Value of one part = 3 × 20 = 60 dozens

### Conclusion
The wholesaler sold **60 dozens** of mangoes at a 20% profit.

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